bell ringer 4-5-17 1. List the 3 ways to prove triangles are similar. 2. When triangles are similar, their corresponding angles are _____ and their corresponding sides are _____. 3. How do you use the proportionality theorms we discussed yesterday?

Proving a quadrilateral is a parallelogram Wednesday, April 5, 2017 (& Thursday, April 5, 2017)

Parallelogram properties Definition – A quadrilateral with opposite sides parallel. TH – Opposite sides are congruent. TH – Opposite angles are congruent. TH – Consecutive angles are supplementary. TH – Diagonals bisect each other. CONVERSES are true!!!

Proving A quadrilateral is a parallelogram 1. If opposite sides are parallel… 2. If opposite sides are congruent... 3. If opposite angles are congruent... 4. If ONE angle is supplementary to BOTH consecutive angles... 5. If the diagonals bisect each other... 6. If ONE pair of opposite sides are BOTH congruent and parallel...

Proofs (p.136) A two-column proof is preferred although flow proofs and paragraph proofs exist. It lists statements on the left and reasons on the right. ALWAYS list the Given first and the Prove last. Some other things we use in proofs are: - Reflexive Property – anything is congruent to itself - Transitive Property – If a = b and b = c, then a = c. - CPCTC – corresponding parts of congruent triangles are congruent - Other definitions, postulates, and theorems

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What is the first thing you list when writing a proof? exit ticket What is the first thing you list when writing a proof? What is the last thing you list when writing a proof? Homework  Parallelograms and Properties Proofs